The analysis of self-excited combustion instabilies encountered in a laboratory-scale, swirl-stabilized combustion system is presented. The instability is successfully captured by reactive large-eddy simulation (LES) and analyzed by using a global acoustic energy equation. This energy equation shows how the source term due to combustion (equivalent to the Rayleigh criterion) is balanced by the acoustic fluxes at the boundaries when reaching the limit cycle. Additionally, an Helmholtz-equation solver including flame-acoustics interaction modeling is used to predict the stability characteristics of the system. Feeding the flame-transfer function from the LES into this solver allows to predict an amplification rate for each mode. The unstable mode encountered in the LES compares well with the mode of the highest amplification factor in the Helmholtz-equation solver, in terms of mode shape as well as in frequency.